A typical ball nose, end mill such as shown in FIG. 1, generally referenced 10, includes a shank 12, straight or conical cutting portion 14 and rounded cutting portion 16. The cutting speed at the rounded portion 16 of a ball nose end mill is gradually decreasing from the full diameter 18 of the ball towards the tip 20. The cutting speed is directly related to the diameter and can be expressed, with reference to FIGS. 2 and 3, by the equation V=NπDsinθ. Where V is the cutting speed or tangential velocity (meters per second), N is the rotation speed (turns per second), D the full diameter 18 (meters) and θ (referenced 21) is the angle between the longitudinal center line 22 of the tool and any line 24 extending from the center point 26 of the rounded cutting portion 16 to a measured point 28 on the cutting edge 29.
Accordingly the cutting speed is related to the angle θ by the sinusoidal equation, meaning that velocity is near zero adjacent the center of the tool, rapidly increasing in the range of 0°<θ<30° wherein for θ=30° the speed V is half of the maximal speed, and slowly increasing in the range of 30°<θ<90° to the maximal speed at the full diameter 18 of the rounded portion 16.
The cutting edge geometry as viewed in FIG. 4 (a sectional view taken along line A-A of FIG. 3), depicts the rake angle 30, wedge angle 32, and relief angle 34, usually represented by the Greek letters α, β, γ respectively.
Solid High-Speed Steel (HSS) and carbide tools traditionally finished by the grinding process, typically have constant rake, wedge and relief angles along the cutting edge 29 of the rounded portion 16. As a result, each A-A section as in FIG. 3 taken at different θ values will have the same angles α, β, γ.
Modern grinding techniques permit more flexibility in shaping the relief angle. An example is suggested in U.S. Pat. No. 5,558,475, disclosing a tool with constant positive rake angle α of size +8°±2° along the whole radius and a continuous, dimension depending decreasing clearance (relief) angle γ between 17°±2° to 10°±2° towards the center. The rake and clearance angles are measured in a plane perpendicular to the cutting edge. In a preferred embodiment of the above patent, a ball nose end mill has a decreasing clearance angle from 15° to 10° from the periphery to the center.
The introduction of disposable carbide inserts to ball nose and bull nose end mills has permitted even more complex structures. Such a structure is described for example in U.S. Pat. No. 6,024,519, disclosing a throwaway insert for a ball end mill with sloped rake faces, whereby the farther away from the noses, the steeper the rise of the rake faces from the groove. Thus, the nearer to the side where the cutting speed is higher, the greater the rake angle.
A specific example given in the above patent is a tool having at its periphery rake angle α between 5°-25° and wedge angle β of 85°-65°, the relief angle γ being minimal. Thus, the rake angles at any longitudinal portions of the cutting edge are all positive except the nose portions, wherein the rake angle α is negative.
However, for a tool intended for multi-axis CNC machining with fast horizontal feed rates, a negative or even zero rake angle adjacent the tip 20, exerts very high forces on the machine, the tool and the workpiece. This will he better understood with reference to FIGS. 4 and 5 showing sectional views taken along lines A-A and B-B of FIG. 3, Section B-B taken along a horizontal line parallel to the horizontal feed of the machine represents the actual working section when horizontal feeds are involved. It will be recognized by a person skilled in the art of trigonometry that positive rake and relief angles α, γ, respectively, as viewed in cross-section along a radial line to any point 28 along the cutting edge 29 (as shown in FIG. 4), will appear smaller (α1<α, γ1<γ) when viewed in a section parallel to the horizontal through same point 28 along the cutting edge 29, as shown in FIG. 5.
Thus, the combination of low cutting speed adjacent to the tip 20 of the tool with the geometrically reduced horizontal feed rake and relief angles as explained above exerts elevated cutting forces, heat and rough surface quality.
In an experimental research made by the present applicant, it has been shown that further optimization of the cutting edge geometry provides better performance, surface quality and extended life of the tool.